Question

Bardzo proszę
Rozwiązać równanie

Answer 1

4sinx*cos²x=2*(2sinxcosx)*cosx=2*sin(2x)*cosx=sin(x)+sin(3x)

sinx-cosx=sinx+sin(3x)
sin(3x)+cosx=0
sin(3x)+sin(π/2-x)=0  v sin(3x)+sin(x-π/2)=0,      cosx=cos(-x)
2sin (2x+π/4)*sin(x+π/4)=0  
sin(2x+π/4)=0  v  sin(x+π/4)=0  v  sin(π/4-x)=0
2x+π/4=kπ  v  x+π/4=kπ  , k∈C
2x=-π/4+kπ v 2x=5π/4+kπ v x=-π/4+kπ v x=5π/4+kπ v x=-5π/8+kπ
x=-π/8+kπ  v  x=-5π/8+kπ v  x=-π/4+kπ